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%I #16 Jul 12 2024 16:35:51
%S 0,0,0,4,36,324,2592,20736,172800,1440000,12960000,116640000,
%T 1143072000,11202105600,119489126400,1274550681600,14748372172800,
%U 170659735142400,2133246689280000,26665583616000000,358503957504000000,4819886539776000000,69406366172774400000
%N a(n) = [n/2]!*[(n+1)/2]!*C([n/2],2)*C([(n+1)/2],2).
%C Number of permutations of n elements with 4 odd displacements.
%C Column 3 of A226288.
%C Column k=4 of A145893, a diagonal of A145894. - _Alois P. Heinz_, May 29 2014
%H R. H. Hardin, <a href="/A226283/b226283.txt">Table of n, a(n) for n = 1..210</a>
%t a[n_]:=(Floor[n/2])!(Floor[(n+1)/2])!Binomial[Floor[n/2],2]Binomial[Floor[(n+1)/2],2]; Array[a,23] (* _Stefano Spezia_, Jul 12 2024 *)
%Y Cf. A145893, A145894, A226288.
%K nonn
%O 1,4
%A _R. H. Hardin_, connection of formula with combinatoric problem via _N. J. A. Sloane_ in the Sequence Fans Mailing List, Jun 02 2013